Answer to Question #120257 in Statistics and Probability for Joseph Se

Question

inferential

6. Suppose we collected a sample of size n = 100 from some population and used the data to calculate a 95% confidence interval for the population mean. Now suppose we are going to increase the sample size to n = 300. Keeping all else constant, which of the following would we expect to occur as a result of increasing the sample size?

1. The standard error would decrease.
2. Width of the 95% confidence interval would increase.
3. The margin of error would decrease.

A. II and III
B. I and III
C.I and II
D.I, II, and III

Answer 1

The standard error: $\sigma_M=\dfrac{\sigma}{\sqrt{n}}$

The margin of error: $margin \ of\ error=z_c\times\dfrac{\sigma}{\sqrt{n}}$

The width of the confidence interval is twice the margin of error.

Keeping all else constant, which of the following would we expect to occur as a result of increasing the sample size?

The standard error would decrease, the margin of error would decrease, and width of the 95% confidence interval would decrease.

B. I and III